Question

A closed pipe has certain frequency. Now its length is halved. Considering the end correction, its frequency will now become

• A. double
• B. more than double
• C. less than double
• D. four times

Answer 1

Answer: (C)

For a closed pipe,
$f_n=\frac{(2n-1)v}{4(L+D)},$
where, $f_n$ is the frequency,
$n=$ integer,
$v=$ velocity;
$L=$ length of the pipe and
$D=$ diameter of the pipe.
When length is halved, the frequency becomes, $f_n^{\prime }=\frac{(2n-1)v}{4[(L/2)+D)]}$
Comparing these two equations, we can say frequency will become little less than double.